Fast covariance matrix generation
First Claim
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1. A computer-implemented method of generating a covariance matrix associated with a media object, wherein the covariance matrix describes the covariance between data elements in sub-portions of the media object, the method executed by a computing system including a memory in which the media object is stored, and comprising:
- automatically identifying a plurality of relative displacements between pairs of data elements within spatial/temporal data of the media object;
for each one of the plurality of relative displacements, automatically generating a corresponding covariance sum, to produce a plurality of covariance sums;
storing the plurality of covariance sums in a lookup table in the memory, each of the covariance sums stored in the lookup table in association with its corresponding relative displacement to allow retrieval of the covariance sum given the relative displacement;
automatically populating a covariance matrix associated with the media object by retrieving covariance sums from the lookup table using the relative displacements, and writing the retrieved covariance sums to the covariance matrix; and
storing the covariance matrix in the memory of the computing system.
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Abstract
A covariance matrix associated for a set of spatial and/or temporal sub-portions of a media object is populated based on a lookup table of relative displacements and sums of covariance values generated from pairs of data elements in the media object. The lookup table is generated in linear time, providing an efficient method of generating the covariance matrix.
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Citations
45 Claims
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1. A computer-implemented method of generating a covariance matrix associated with a media object, wherein the covariance matrix describes the covariance between data elements in sub-portions of the media object, the method executed by a computing system including a memory in which the media object is stored, and comprising:
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automatically identifying a plurality of relative displacements between pairs of data elements within spatial/temporal data of the media object; for each one of the plurality of relative displacements, automatically generating a corresponding covariance sum, to produce a plurality of covariance sums; storing the plurality of covariance sums in a lookup table in the memory, each of the covariance sums stored in the lookup table in association with its corresponding relative displacement to allow retrieval of the covariance sum given the relative displacement; automatically populating a covariance matrix associated with the media object by retrieving covariance sums from the lookup table using the relative displacements, and writing the retrieved covariance sums to the covariance matrix; and storing the covariance matrix in the memory of the computing system. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
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16. A non-transitory computer-readable storage medium encoded with executable computer program code for generating a covariance matrix associated with a media object, wherein the covariance matrix describes the covariance between data elements in sub-portions of the media object, the program code comprising instructions for:
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automatically identifying a plurality of relative displacements between pairs of data elements within spatial/temporal data of the media object; for each one of the plurality of relative displacements, automatically generating a corresponding covariance sum, to produce a plurality of covariance sums; storing the plurality of covariance sums in a lookup table in a memory, each of the covariance sums stored in the lookup table in association with its corresponding relative displacement to allow retrieval of the covariance sum given the relative displacement; automatically populating a covariance matrix associated with the media object by retrieving covariance sums directly from the lookup table using the relative displacements, and writing the retrieved covariance sums to the covariance matrix; and storing the covariance matrix in the memory. - View Dependent Claims (17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30)
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31. A computer system for generating a covariance matrix associated with a media object, wherein the covariance matrix describes the covariance between data elements in sub-portions of the media object, the computer system comprising:
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a memory; a processor; a covariance matrix generation module configured to; automatically identify a plurality of relative displacements between pairs of data elements within spatial/temporal data of the media object; for each one of the plurality of relative displacements, automatically generate a corresponding covariance sum, to produce a plurality of covariance sums; store the plurality of covariance sums in a lookup table in the memory, each of the covariance sums stored in the lookup table in association with its corresponding relative displacement to allow retrieval of the covariance sum given the relative displacement; automatically populate a covariance matrix associated with the media object by retrieving covariance sums from the lookup table using the relative displacement, and write the retrieved covariance sums to the covariance matrix; and store the covariance matrix in the memory. - View Dependent Claims (32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45)
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Specification